A GCV based method for nonlinear ill-posed problems

This paper discusses the inversion of nonlinear ill-posed problems. Such pr oblems are solved through regularization and iteration and a major computat ional problem arises because the regularization parameter is not known a pr iori. In this paper we show that the regularization should be made up of tw o parts. A global regularization parameter is required to deal with the mea surement noise, and a local regularization is needed to deal with the nonli nearity. We suggest the generalized cross validation (GCV) as a method to e stimate the global regularization parameter and the damped Gauss-Newton to impose local regularization. Our algorithm is tested on the magnetotelluric problem. In the second part of this paper we develop a methodology to implement our algorithm on large-scale problems. We show that hybrid regularization metho ds can successfully estimate the global regularization parameter. Our algor ithm is tested on a large gravimetric problem.